Question: Simplify the following expression: $ n = \dfrac{-9y - 9}{y - 1} + \dfrac{1}{8} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{8}{8}$ $ \dfrac{-9y - 9}{y - 1} \times \dfrac{8}{8} = \dfrac{-72y - 72}{8y - 8} $ Multiply the second expression by $\dfrac{y - 1}{y - 1}$ $ \dfrac{1}{8} \times \dfrac{y - 1}{y - 1} = \dfrac{y - 1}{8y - 8} $ Therefore $ n = \dfrac{-72y - 72}{8y - 8} + \dfrac{y - 1}{8y - 8} $ Now the expressions have the same denominator we can simply add the numerators: $n = \dfrac{-72y - 72 + y - 1}{8y - 8} $ $n = \dfrac{-71y - 73}{8y - 8}$